Answer
Potential-energy function is a downward parabola. The equilibrium is unstable.
Work Step by Step
We know that conservative force is the negative of the corresponding potential energy. So the potential-energy function for the force $F_{x}=+kx$ is an integral of this function and it equals $-kx^{2}/2$. Thus the result is a downward parabola where potential energy is a maximum at $x=0$. Any maximum in a potential-energy curve is an unstable equilibrium position.
